Paper Info
Title
Denoising images: non-linear leap-frog for shape and light-source recovery
Abstract
In 3-source photometric stereo, a Lambertian surface is illuminated from 3 known independent light-source directions, and photographed to give 3 images. The task of recovering the surface reduces to solving systems of linear equations for the gradients of a bivariate function u whose graph is the visible part of the surface [9], [16], [17], [24]. In the present paper we consider the same task, but with slightly more realistic assumptions: the photographic images are contaminated by Gaussian noise, and light-source directions may not be known. This leads to a non-quadratic optimization problem with many independent variables, compared to the quadratic problems resulting from addition of noise to the gradient of u and solved by linear methods in [6], [10], [20], [21], [22], [25]. The distinction is illustrated in Example 1 below. Perhaps the most natural way to solve our problem is by global Gradient Descent, and we compare this with the 2-dimensional Leap-Frog Algorithm [23]. For this we review some mathematical results of [23] and describe an implementation in sufficient detail to permit code to be written. Then we give examples comparing the behaviour of Leap-Frog with Gradient Descent, and explore an extension of Leap-Frog (not covered in [23]) to estimate light source directions when these are not given, as well as the reflecting surface.
Year
DOI
Venue
2002
10.1007/3-540-36586-9_27
Theoretical Foundations of Computer Vision
Keywords
Field
DocType
independent variable,independent light-source direction,lambertian surface,linear equation,bivariate function u,gradient descent,2-dimensional leap-frog algorithm,light-source recovery,light-source direction,non-linear leap-frog,denoising image,global gradient descent,gaussian noise,photometric stereo,quadratic optimization,2 dimensional,linear equations
Noise reduction,Applied mathematics,Gradient descent,Nonlinear system,System of linear equations,Quadratic equation,Geometry,Gaussian noise,Optimization problem,Photometric stereo,Mathematics
Conference
Volume
ISSN
ISBN
2616
0302-9743
3-540-00916-7
Citations 
PageRank 
References 
7
0.57
12
Authors
2
Name
Order
Citations
PageRank
Lyle Noakes114922.67
Ryszard Kozera216326.54